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The fact that the thing being broken into is a compound noun (the middle of a piece of music) might throw some people, so it's easier to just consider...

The announcer broke into the music

Some native speakers (me, at least) would be happy with broke in on the music, because to break in is an established phrasal verb meaning to interrupt. It doesn't necessarily need to be followed by a noun phrase identifying what was broken into (often, it's just an implied ongoing conversation). But if the "thing being interrupted" is specified, it should be introduced with its own preposition (i.e. - on).

Personally I see no real syntactic difference between break into the music and break into the house (the "integrity" of the music/house is broken/violated in much the same way). So it's worth noting that Google Books claims 265,000 hits on that link, as compared to just 168 results for break in the house.

As per this Cambridge Dictionaries page,

We use in to talk about where something is in relation to a larger area around it:

A: Where’s Jane?
B: She’s in the garden.

I’ve left my keys in the car.

We use into to talk about the movement of something, usually with a verb that expresses movement (e.g. go, come). It shows where something is or was going:

A: Where’s Jane?
B: She’s gone into the house.

Helen came into the room.

Compare:

She’s gone for a walk in the garden. (She is in the garden walking.) She walked into the garden. (She entered the garden.)

With some verbs (e.g. put, fall, jump, dive) we can use either in or into with no difference in meaning:

Can you put the milk in/into the fridge? Her keys fell in/into the canal.

However, even with a verb like put, some additional context can favor the use of one preposition over the other:

• I put my hands in/into my pockets to keep them warm.
• Slowly, he put his hand into his pocket and snuck out a folding knife.

In the second example, we're placing emphasis on the movement of the hand, so into appears to be more appropriate than just in.